Described below is a method for reducing Peak-to-Average Power Ratio in an OFDM transmission system.
One of the promising technologies for mobile communications systems beyond 3G (B3G) is multi-carrier modulation based on Orthogonal Frequency Division Multiplex (OFDM). Among other expected features like interactive multimedia services, high capacity, etc., the most crucial seems to be the capability of reaching much higher date rates than it is achievable with current 2G and 3G mobile communications systems. Currently, a considerable number of studies on B3G systems are based on an objective to achieve data rate up to 100 Mbit/s. Assuming typical phenomena of mobile channels like reflections, diffractions and scattering of a propagated radio signal, makes the goal of higher data rates even harder. For single carrier systems data rate of 100 Mbits/s means drastic reduction of symbol duration. If the channel delay spread exceeds the symbol duration then such a system is subject to inter-symbol interference (ISI) caused by a frequency selective fading, and without advanced equalization it is practically unusable.
The basic idea of OFDM is to divide the transmitted bit stream into many different sub-streams and send these over many different sub-channels (sub-carriers). The data rate on each of the sub-channels is much less than the total data rate, and the corresponding sub-channel bandwidth is much less than the total system bandwidth. The number of sub-streams is chosen in a way ensuring that each sub-channel has a bandwidth less than the coherence bandwidth of the channel. Hence, the sub-channels experience relatively flat fading and channel induced ISI on each sub-channel is small.
On the other hand, OFDM can be considered as a technique that transmits data in parallel on a number of equally spaced sinusoidal waveforms which means that the data to be transmitted determine the relative phases of the sinusoids. This results in the main drawback. If the amplitudes of the sinusoids occur at the same time, they add up most constructively producing high peak in resulted signal, greatly exceeding the average level. Since the peak in the signal level defines the peak in the power of the signal, a power amplifier (PA) has to track these peaks in order not to produce distortion. This leads to uneven demands on PA, e.g. it operates most of the time at levels much below its capacity which degrades energy efficiency.
In order to quantify the power peak, the use of the so called Peak-to-Average Power Ratio (PAPR), which is defined in dB as the power peak value relative to the average power of the signal, is made. Such a definition is widely accepted and reasonable also in other systems dealing with high signal peak values.
There is a wide range of methods developed to combat the problem of high PAPR. The most promising methods are based on coding.
The idea of these techniques is to avoid the transmission of symbols that exhibit high PAPR by a properly chosen coding, as described in S. H. Han, J. H. Lee, “An overview of Peak-To-Average Power Ratio Reduction Techniques for Multicarrier Transmission”, IEEE Wireless Communications, April 2005, pp. 56-65. A common example was originally presented in A. E. Jones, T. A. Wilkinson and S. K. Barton, “Block Coding Scheme for Reduction of Peak to Mean Envelope Power Ratio of Multicarrier Transmission Schemes”, Elect Letters, Vol. 30, No. 25, December 1994, pp. 2098-2099. It is shown that for the case of BPSK (Binary Phase Shift Keying) modulation and 4 sub-carriers, PAPR in the worst case is 6.02 dB. They noticed that by proper coding (one redundant bit out of four) they would be able to avoid data sequences which exploit high PAPR, resulting in the 3.54 dB PAPR gain. Unfortunately, for a number of sub-carriers greater than 4, they were unable to guarantee the same PAPR gain using simple coding, but were forced to perform an exhaustive search to find the best sequences and make use of look-up tables thereafter. However, such a solution proves infeasible for practical purposes, since length of the look-up table grows rapidly as the number of sub-carriers increases.
Slightly improved approach is to use code words drawn from offsets of a linear code. The code is chosen for its error correction capabilities, whereas the offset to reduce the PAPR of the resulting signals. Algorithm is easy to implement, but requires extensive calculations to find good codes and offsets, as described in A. E. Jones and T. A. Wilkinson, “Combined Coding for Error Control and Increased Robustness to System Non-linearities in OFDM”, Proc. IEEE VTC '96, Atlanta, Ga., April-May 1996, pp. 904-908. Even though a computationally efficient geometrical approach to offset selection was proposed in V. Tarokh and H. Jafarkhani, “On the Computation and Reduction of the Peak-to-Average Power Ratio in Multicarrier Communications”, IEEE Trans. Commun., Vol. 48, No. 1, January 2000, pp. 37-44, this does not guarantee the PAPR reduction.
Another attractive way is to employ Golay complementary sequences, which provide ideal value of PAPR (no greater than 2 dB), as code words. It has been shown in J. A. Davis and J. Jedwab, “Peak-To-Mean Power Control and Error Correction for OFDM Transmission Using Golay Sequences and Reed-Muller Codes”, Elect. Letters, Vol. 33, No. 4. February 1997, pp. 267-268; and J. A. Davis and J. Jedwab, “Peak-To-Mean Power Control in OFDM, Golay Complementary Sequences, and Reed-Muller Codes, “IEEE Trans. Info. Theory”, Vol. 45, No. 7, November 1999, pp. 2397-2417 that large set of binary length 2m; m ε N Golay complementary pairs can be obtained from the second-order Reed-Muller code. Consequently, it seems possible to combine Reed-Muller block coding (including error control capabilities) along with Golay complementary sequences providing good PAPR. Anyway, this can only be done for the case of MPSK modulation and is again infeasible for large number of sub-carriers due to computations complexity. Moreover, the code rate also decreases with the number of sub-carriers.
Recently, a new method called complement block coding has been proposed in T. Jiang and G. Zhu, “Complement Block Coding for reduction in Peak-to-Average power Ratio of OFDM Signals”, IEEE Comm. Mag., September 2005, pp. S17-S22. It uses simple bit inversions of certain bits on predefined positions. It is claimed to obtain interesting PAPR reduction of at most 3.5 dB. In this method, the code rate can be kept constant. Advantageous simplicity of the encoding operation does not, however, guarantee the PAPR gain for any number of sub-carriers. What is more, error correction capabilities of the code are limited to correcting only those bits that had been complemented.
To sum up, all the methods mentioned above do reduce PAPR for the cost of sacrificing other parameters. They introduce a lot of overhead (Reed-Muller code) or do not guarantee PAPR low enough at all. The main disadvantage, however, is that they are impractical for large numbers of sub-carriers due to either high complexity or small PAPR gain.